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• Problem: Prove or disprove: 10" = o(n!)

• Problem: Prove or disprove: 10" = o(n!)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This question is under Big O notation topic. 

Little o notation • Let f(x) and g(x) be nonnegative real-valued functions on the positive real numbers, and suppose that g(x) is strictly positive for all x sufficiently large • We define f (x) = o(g(x)) if for every constant c >0 there exists a constant d such that f(x) < cg(x) for all x > d. • Another way to say that is: f(x) = o(g(x)) if limx→ • Example: If f(x) = 3x + /x and g(x) = 5x, then f(x) >g(x) and g(x) > f(x) for all x > 0. Thus f(x) + o(g(x)) and g(x) t o(f(x)) f (x) og(x) Example: If a(x) = /x and b(x) = x, then a(x) = o(b(x)) since a(x) < cb(x) for all c < 1 and x >2. However, b(x) # o(a(x)) since x > Vx for all x > 0. Problem: Prove or disprove: 10" = o(n!) 1
Transcribed Image Text:Little o notation • Let f(x) and g(x) be nonnegative real-valued functions on the positive real numbers, and suppose that g(x) is strictly positive for all x sufficiently large • We define f (x) = o(g(x)) if for every constant c >0 there exists a constant d such that f(x) < cg(x) for all x > d. • Another way to say that is: f(x) = o(g(x)) if limx→ • Example: If f(x) = 3x + /x and g(x) = 5x, then f(x) >g(x) and g(x) > f(x) for all x > 0. Thus f(x) + o(g(x)) and g(x) t o(f(x)) f (x) og(x) Example: If a(x) = /x and b(x) = x, then a(x) = o(b(x)) since a(x) < cb(x) for all c < 1 and x >2. However, b(x) # o(a(x)) since x > Vx for all x > 0. Problem: Prove or disprove: 10" = o(n!) 1
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